On the limiting behavior of randomly weighted partial sums

We study the almost sure limiting behavior and convergence in probability of weighted partial sums of the form where {W_nj, 1jn, n1} and {X_nj, 1jn, n1} are triangular arrays of random variables. The results obtain irrespective of the joint distributions of the random variables within each array. Applications concerning the Efron bootstrap and queueing theory are discussed.     

Two-phase optimization of coal strategies at a power station

Development of optimal coal mining and stockpiling strategies for a new 960 MW thermal power station depends strongly on the operation of New Zealand's mixed hydro/thermal power system. To overcome the large dimensionality of the problem the optimization proceeds in two phases for each future scenario studied. Phase 1 finds optimal hydro operating strategies with thermal generation in merit order of marginal fuel costs. It uses stochastic dynamic programming. The hydro generating strategies are used as input to the phase 2 stochastic simulation of the coal mining and stockpiling operation at the new thermal station. Finally, a strategy is identified which is a priori best over all future scenarios of industrial development and oil prices studied.     

H^—5的正四面体中心和正方形中心构型能量的理论计算

文中用ＭＡＣＱＭ（ｍｏｄｉｆｉｅｄａｒａｎｇｅｍｅｎｔｃｈａｎｎｅｌｑｕａｎｔｕｍｍｅｃｈａｎｉｃｓ）方法计算了负离子团簇Ｈ－５的正四面体中心和正方形中心构型的能量随中心原子核到顶角原子核间距离Ｒ变化的曲线。计算得知，两种构型均在Ｒ＝１．５５ａ０时有能量极小值Ｅ正四面体中心＝－２．７８９９ａ．ｕ．，Ｅ正方形中心＝－２．７５３９ａ．ｕ．。说明Ｈ－５的这两种结构都可能存在，但正四面体中心结构较为稳定。     

Estimate of exponential convergence rate in total variation by spectral gap

This note is devoted to study the exponential convergence rate in the total variation for reversible Markov processes by comparing it with the spectral gap. It is proved that in a quite general setup, with a suitable restriction on the initial distributions, the rate is bounded from below by the spectral gap. Furthermore, in the compact case or for birth-death processes or half-line diffusions, the rate is shown to be equal to the spectral gap. Research supported in part by NSFC, Qiu Shi Sci. & Tech. Found. DPFIHE, MCSEC and Univ., of Rome I, Italy     

相空间中的Noether定理及其应用

从修改的哈密顿变分原理出发导出相空间的 Noether 定理,对正则拉氏量系统,分析该系统在相空间中的对称性质,可导出其相应的守恒量,而这种相空间中的对称性质在位形空间中常常又是不呈现出来的.对奇异拉氏量系统,该系统具有 Dirac约束,我们分析了约束系统的对称性质,讨论了 Dirac 猜想是否有效.     

Estimation of the scale parameter of a power law process using power law counts

Analogous to Kingman's Poisson Counts, power law counts are defined. Further, these are used to obtain the maximum likelihood estimator of the scale parameter of a power law process. Comparison of this estimator is done with those obtained by using other sampling schemes. Also, cost comparisons are done under the assumption of equal asymptotic variances under different sampling schemes.Work done while the author was with the Department of Statistics, University of Poona. Current address: Dept. of Mathematics, CME, Pune.     

The design of a Tort law to control accidents

In this paper we analyse a two-stage game involving the government and n agents who engage in a single activity (driving). The government establishes the legal policy setting and the agents proceed to play a non-cooperative game of incomplete information with a risk of accident in which their behavioral strategy is their level of care. We examine the Nash-equilibrium conditions for single-activity accidents between heterogeneous agents, ‘good’ drivers or ‘bad’ drivers allowing a variable damage function and a liability rule defined on the cube. The relative desirability for society of alternative equilibria and the conditions under which they can obtain are discussed. The constraints which circumscribe the ability of the government to induce an equilibrium involving careful driving are demonstrated. It transpires that when the proportion of good drivers increases, it becomes more difficult to sustain a careful equilibrium whereas an equilibrium of reckless behavior becomes easier to sustain. Various extensions of the models are also presented.     

Entrance laws for Feller diffusions on (0, ∞) and Doob's h-path transformation

We consider the problem of constructing entrance laws for Feller diffusions on the state space (0, ∞). Our method, based on Feller-McKean theory of one-dimensional diffusions, gives an analytic expression for the entrance density in terms of transition density. Moreover, the entrance density is the density of the first passage time to the left boundary {0}. Also, the entrance density is related to the transition density via Doob's h-path transformation.     

Partial molar isentropic compressibilities and volumes of selected electrolytes and nonelectrolytes in dimethylsulfoxide

Precision densities and sound velocities for solutions of selected univalent electrolytes and nonelectrolytes in DMSO have been measured at 25°C, and apparent molar isentropic compressibilities and volumes evaluated. The data were extrapolated to infinite dilution to obtain standard state partial molar quantities, K _s,2 ^° , and V ₂ ^° . Values of V ₂ ^° and K _s,2 ^° for alkali metal halides in DMSO are very similar to those in water. The results confirm conclusions derived from data in water and other nonaqueous solvents that K _s,2 ^° and V ₂ ^° for alkali metal halides are strongly dependent on solvent compressibility. K _s,2 ^° becomes more negative and V ₂ ^° decreases as solvent compressibility increases. Attempts to determine ionic K _s,2 ^° values suggest that a significant dissymmetry exists between ₄P⁺ and ₄B^– in DMSO, whereas in water and MeOH, these large ions appear to behave similarly. Ionic V ₂ ^° values support this conclusion. Steric hindrance in the DMSO molecule is believed to be responsible for this dissymmetry.     

A universal scaling law for hadronic reactions

A master scaling law is proposed for arbitrary distributions in arbitrary hadronic processes of which all experimentally established scaling laws (and a host of others, easily deduced as occasion demands) are special cases.